Prosody is the syllabic qualities of speech, here referring primarily to syllable weight and accent. The placement and type of syllable stress varies on the language, dialect, and time period.
Insular Celtic languages are stress-accent languages, in contrast to pitch-accent (such as Proto-Indo-European, Sanskrit, and Attic Greek). The accents of Continental Celtic languages are not generally known, other than that Gaulish can be supposed to have had stress accents in its late phases. Proto-Celtic is even more uncertain, and arguments have been advanced for either pitch or stress accent.
Sound changes such as apocope and lenition are primary sources of evidence for stress accents. Apocope in particular can also have a decisive impact on changing the accent placement system. For example, a penultimate (second-to-last syllable) stress will naturally be transformed into an oxytonic (final syllable) stress immediately following the loss of inflected endings:
PBr. *ke·'ne·tlon > LPBr. *ke·'nedl.
Other agents responsible for shifting the placement of stress accent over the course of a language’s development are less clear. Some evidence may suggest the influence of Latin and perhaps also Greek as a factor in producing Late Gaulish’s penultimate and antepenultimate stress systems. Latinization may likewise have shifted Brittonic from initial (first syllable) stress to penultimate, though the periodization of this change is debated. Old Irish remained stress-initial.
Peter Schrijver provides evidence that demonstrates an initial stress phase for Early Proto-Brittonic, including during the period when Brittonic first began acquiring Latin loanwords (1st to 2nd Century CE). In consideration of the root-initial stress of Old Irish, he concludes that this “strongly suggests that the system of initial stress [...] goes back at least to Proto-Insular-Celtic times” (perhaps around the 6th Century BCE).
For comparison, Old Latin is thought to have inherited initial stress from Proto-Italic and retained it until around 250 BC. (Debated: theory from Schrijver)
David Stifter observes that analysis of continental Celtic inscriptions which are thought to exhibit verbal art reveals that alliteration is a common practice. Alliterative word pairs are also typical of early Irish poetry. Alliteration, he notes, is particularly suited to initial stress languages, which are known to feature systematic (not just occasional) alliteration. This certainly leaves open the suggestion of an initial stress phase in Gaulish and other Continental Celtic languages. However, it is known that alliteration (like probably all poetic art forms) can be introduced to languages that lack features which might naturally produce it---for example, Classical Armenian, an oxytonic language (Matasović 2009), adopted alliteration in the 10th Century (Hacikyan 2000)---so the possibility of an areal influence from initial stress neighbors (e.g. Insular Celtic or Old Latin) cannot be ruled out.
Then again, the initial stress nature of Continental Celtic’s closest neighbors and relatives could be seen as another argument that initial stress would have existed throughout the Celtic branch at that time. One notable exception to this being that Proto-Germanic is not thought to have shifted from pitch accent to initial stress until sometime later than its first appearance in the 6th Century BCE. (When/why did Norwegian and Swedish develop pitch accents? Supposedly Old Norse inherited a stress accent from P-G).
Metrical classification of certain continental texts which some analysts suppose to be poetic would depend on an initial stress system. However, Stifter points out that the Indo-European nature of Old Celtic favors the production of di- and trisyllabic words, which can easily give the appearance of trochaic or dactylic meters by pure coincidence, even in prose. Thus, attempted metrical analyses of continental inscriptions are likewise inconclusive.
De Bernardo Stempel has produced a theory, based on hydro- and toponymical developments in French, that there were at one time two late Gaulish dialects with differing stress systems. One is thought to have been based in more urban settlements and coastal areas that had greater Mediterranean contact, and to feature antepenultimate stress. The other is thought to have been found in more rural and marginal areas and to feature a (presumably older) penultimate stress. The antepenultimate stress system has also been suggested by Falc’hun to have spread to urban areas of Britain such as London and York at a later date than the development of British penultimate stress. This theory has not gained universal acceptance, however.
The apocope of *-kʷe > -c occurred after the development of *-kʷe > -pe in Lepontic, but prior to the *kʷ > p shift that defines Gaulish. Could this be evidence of a stress accent prior to the development of Gaulish?
Does the loss of word-initial *φ- in Proto-Celtic disprove an initial stress accent?
Does the lenition of *ss or *st > ðð point to a stress accent? What about in word-initial cases (e.g. *St- > Ð-)?
Do languages always inherit the stress system of their parent and only shift later? E.g., Koine Greek and Proto-Germanic were originally pitch accented; Latin, Primitive Irish, and Common Brittonic were originally initial stress like their parents. All of these except Irish later changed either their stress type or stress placement.
When did Proto-Germanic shift to stress accent? Could this have been areal influence from Latin or Celtic?
Modern Welsh acquired its pitch accent after the oxytonic stress of Late Brittonic shifted back to a penultimate stress (Willis). The pitch accent is typically oxytonic, so thought to be a vestige of the older oxytonic stress.
Historical Linguistics gives living language examples of how stress systems are easily and frequently borrowed from unrelated neighboring languages. Stress systems can be considered areal.
Old Irish is assumed to have had a stronger stress accent than Classical Latin, because of how Latin borrowings were syncopated more heavily in Irish than in Latin itself (could the placement have had more of an effect on this than the strength?). Further, it is said that syncopation of Latin was heavier in France and Northern Italy---areas under Celtic influence---than elsewhere in the Romantic sphere, which might point to a heavier stress accent in Celtic (Lindsay 2010).
Most P-C reconstructions feature long vowels consistent with initial stress. Oniga (2014) points out that “a short syllable is not suitable to bear stress” and “cross-linguistically, a stressed vowel tends to be longer than an unstressed one”. However, P-C reconstructions are overwhelmingly derived from Insular Celtic tongues, for which Schrijver has provided evidence of an initial stress in its proto-language. So perhaps these merely reflect the initial stress of Proto-Insular-Celtic rather than Proto-Celtic proper.
Some nuances: The ‘pitch vs. stress accent’ dichotomy conceals the fact that stress accents also have tonal features, including in English. Finish, Hungarian, and Czech are examples of languages with strong stress accents, but which haven’t shown signs of unstressed vowel reduction. While it’s true that exclusively tonal accents will not likely result in vowel reduction (syncope, apocope, etc.), it’s not necessarily the case that a stress accent will cause that. (Sihler 2008)
It’s been said (can’t remember where) that French scholars militate towards a theory of no stress accent in Latin, only tonic (based off probably inaccurate terminology used by Roman authors), while German and English writers typically assume a stress accent. Linguistics clearly shows an initial stress in Old Latin, though new research suggests the possibility of an inherited PIE tonal accent layered on top of it (see Vine). So this explains why many authors will make it sound as if Old Latin had only an initial stress, which would make it confusing as to how it could develop into Classical Latin stress. But in light of the evidence of a tonal accent, this becomes much more obvious.
“In summary then, the best indications of earliest Celtic accentuation seem to point toward initial stress, if still very inconclusively” (Accentual Change and Language Contact)
Hickey (2015) brings up a discussion of O’Rahilly’s analysis of Southern Irish stress accent shift to long vowels and how this relates to “instability” that is present in a language when there are long vowels within unstressed syllables. Read further!
Word Prosodic Systems in the Languages of Europe has a good and concise treatment of all the modern Celtic languages accentuation.